A method for determining the optical properties of a spectacle lens for all visual points is based on a determination of the course of a main ray at each visual point and of the wavefront belonging to this main ray for an extension determined by the pupil diameter. The wavefront can be considered to be known when it is sufficiently known within a specific approximation, e.g. when Zernike coefficients can be indicated for the wavefront up to a specific order. This order can be the second order if the prismatic power, the refractive power, and the astigmatism are exclusively relevant, the third order if coma and trefoil are to be considered as well, the fourth order if the spherical aberration is to be considered as well, or even a higher order.
It is known from the prior art to determine the shape or form of these wavefronts for optical elements, and in particular for spectacle lenses, which are restricted by at least two refractive boundary surfaces. For example, this can be accomplished by numerically calculating a sufficient number of neighboring rays, along with a subsequent fit of the wavefront data by Zernike polynomials. A different approach is based on a local wavefront tracing (cf. WO 2008 089999 A1). Here, only one single ray (the main ray) is calculated per visual point, and concomitantly the derivatives of the vertex depth of the wavefront with respect to the transversal coordinates (perpendicular to the main ray). These derivatives can be created up to a specific order, the second derivatives describing the local curvature properties of the wavefront (such as refractive power, astigmatism) and the higher derivatives being related to the higher-order aberrations.
With a tracing of light through a spectacle lens, the local derivatives of the wavefront are calculated at a suitable position in the ray path in order to compare them there with desired values resulting from the refraction data of the spectacle lens wearer. This position can be the vertex sphere, for example. To this end, it is assumed that a spherical wavefront originates at an object point and propagates to the first spectacle lens surface. The wavefront is refracted there and subsequently propagates to the second spectacle lens surface, where it is refracted again. If further surfaces are present, the alternation of propagation and refraction is continued until the last boundary surface has been passed. The last propagation takes place from this last boundary surface to the vertex sphere.
WO 2008 089999 A discloses the laws for refraction on refractive surfaces not only for second-order aberrations or optical properties, but also for higher orders. If a wavefront with local derivatives known up to a specific order is incident on a boundary surface in an oblique manner, then the local derivatives of the outgoing wavefront can be calculated up to the same order by means of the calculation methods according to WO 2008 089999 A1. Such a calculation, in particular up to the second order, is important to the assessment of the image formation properties or optical properties of a spectacle lens in its wearing position. In particular, such a calculation is of great importance if a spectacle lens in its wearing position is to be optimized over all visual points.
To improve optical elements/systems, and in particular spectacle lenses, it may be advantageous to additionally introduce optical components into the ray path, which are based on other physical effects than a mere refraction at a curved boundary surface. For example, it is known from the prior art to use diffractive optical elements (DOE) to reduce the color fringe (i.e. the lateral chromatic aberration and/or the chromatic aberration) of image-forming systems/elements. However, if at least one of the boundary surfaces of an image-forming system/element is configured in a more complicated way, for example by including a diffraction grating, then the prior art laws relating to the refraction cannot be applied here.
In the case of an optical element/system with at least one diffraction grating, it has not been possible so far to perform a precise wavefront tracing. This means that the advantages of a diffraction grating cannot be used to the fullest. Specifically, according to the prior art, a refractive error possibly resulting from the introduction of the diffraction grating could at best be calculated very generally, vaguely, and in any way not precisely in the wearing position. In the case of an optical element with at least one phase-modifying (phase-delaying or phase-modulating) element, it is also not possible to perform a precise wavefront tracing with the methods known.
It is an object of the invention to provide a method and a corresponding device, which allow performing a fast and efficient tracing of the optical properties of an arbitrary optical element or system with at least one phase-modifying optical element.